Sorry for the title but I can't come up with another one...

...

Suppose X and Y are simplicial sets and $f : X \rightarrow Y$ is a map such that:

1.) f maps dimensions the right way, that is for all $ n \in \mathbb{N}^0$ we have $f_n := f : X_n \rightarrow Y_n$

2.) f commutes with all face maps in all dimensions, that is $f_{n-1} \circ d^n_k = d^n_k \circ f_n$ for all $n,k \in \mathbb{N}^0$ with $k \leq n$

3.) $f$ commutes with the degeneracy $s_n$ that is $f_{n+1}s_n=s_nf_n$ in any dimension $n \in \mathbb{N}^0$

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(EDIT: So up to this point we only know about commutation with ONE degeneracy)
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Is $f$ a simplicial morphism?

( In my particular situation X and Y are Kan in addition and moreover X is 2-coskeletal and Y is n-coskeletal for n>=2 )

If this only holds under additional assumptions, feel free to write just about that particular situation.

lastdegeneracy s_n. So it's not obviously a simplicial map/morphism. – Tom Leinster Nov 21 '11 at 22:17